$7\mathrm{.}2.$ Cody Gets His Outback

Cody Andrews, a $27-$year$-$old living in Richmond, Virginia, has been a high$-$school teacher for $5$ years. For the past four months, he's been thinking about buying a Subaru Outback, but he feels that he can't afford a brand$-$new one. Recently, however, his friend Devin Carpenter has offered to sell Cody his fully loaded Subaru Outback. Devin wants $$26,900$ for his Outback, which has been driven only $8,000$ miles and is in very good condition. Cody is eager to buy the vehicle but has only $$10,000$ in his savings account at Central Bank. He expects to net $$8,000$ from the sale of his Chevrolet Malibu, but this will still leave him about $$8,900$ short. He has two alternatives for obtaining the money:

Borrow $$8,900$ from the First National Bank of Richmond at a fixed rate of $6$ percent per annum, simple interest. The loan would be repaid in equal monthly installments over a $3-$year $(36-$month$)$ period.

Obtain an $$8,900$ installment loan requiring $36$ monthly payments from the Richmond Teacher's Credit Union at a $4\mathrm{.}5$ percent stated rate of interest. The add$-$on method would be used to calculate the finance charges on this loan.

Critical Thinking Questions

$1.$ Using a financial calculator or a spreadsheet, determine the required monthly payments if the loan is taken out at First National Bank of Richmond.

$2.$ Compute $($a$)$ the finance charges and $($b$)$ the APR on the loan offered by First National Bank of Richmond.

$3.$ Determine the size of the monthly payment required on the loan from the Richmond Teacher's Credit Union.

$4.$ Compute $($a$)$ the finance charges and $($b$)$ the APR on the loan offered by the Richmond Teacher's Credit Union.

$5.$ Compare the two loans and recommend one of them to Cody. Explain your recommendation.